The main aim of this paper is devoted to derive some relations of Gegenbauer matrix polynomials of two variables. Volterra integral equation and a new representation of these matrix polynomials are given here. We introduce new generalized various forms of Gegenbauer matrix polynomials of two and three matrices by using the method of integral transforms to Hermite matrix polynomials. Furthermore, families of generating matrix functions are obtained and their applications are presented.

This paper is developed to study of new families of an extension of the generalized Bessel-type matrix polynomials with three, four and ve matrices by using the various families of integral representation method. An interesting further qualitative properties of this integral representations method are given. Subsequently, explicit formulas for the extended generalized Bessel matrix polynomials and their interesting properties are investigated.

The main goal of this paper is to define and study of Rainville’s matrix polynomials. The integral form, typical families of linear, bilinear and bilateral generating matrix functions are obtained and gives expansions of these polynomials. The active differential operator on Rainville’s matrix polynomials and their applications, some matrix recurrence relations are derived and the matrix differential equation is obtained. Subsequently, Rodrigues formula are then developed for Rainville’s matrix polynomials. Furthermore, we give the generating matrix functions for Rainville’s matrix polynomials, involving the Horn’s matrix functions of two variables and hypergeometric matrix functions of three variables.

This paper is motivated by an open problem of several inequalities for confluent hypergeometric functions. We give some inequalities for simple Laguerre, Laguerre, pseudo-Laguerre, Shively’s pseudo-Laguerre, and Hermite functions of one and two variables.

Forty-nine species and two species varieties belonging to 22 genera isolated on glucose and 1% crude oil Czapek's agar medium from 48 soil samples contaminated with mazot and solar collected from three governorates in Upper Egypt namely, El-Minya, Assiut and Sohag. The most common genus was Aspergillus which isolated from three governorates and from both soil types, while the most common species was Aspergillus fumigatus on mazot polluted soil and Aspergillus flavus, Aspergillus fumigatus and Aspergillus terreus on solar polluted soils. Out of these fungal species, 40 isolates were tested for their ability to utilize crude oil in liquid culture at 28 ±1ºC. Only 32 isolates subjected to lipase activity test. Remarkably, on these tested isolates 35 isolate have been grown, 5 isolates have been growing without producing the enzyme and 5 isolates not grown. The highest lipase activity observed by Fusarium verticilloides giving 12.28 U/ml.

A total of 230 fungal isolates were recovered from rhizosphere, rhizoplane, phyllosphere, phylloplane and seeds of maize (Zea mays L.) plants cultivated in different localities in Assiut Governorate (Abnob, Elbadary, Elfath, Assiut and El qosea).The isolates belonging to 15 genera, 35 species and one variety. The most dominant genus was Aspergillus whereas the most common species were A. terreus and A. flavus. A representative isolates of A. terreus were tested for riboflavin production using two different types of synthetic media. It was observed that most isolates (9 out of 12 isolates) produced riboflavin, but the highest yield on YPD medium (60 mg/l) obtained from A. terreus (isolate No. 9) which isolated from rhizoplane of maize plants.

A total of 230 fungal isolates were recovered from rhizosphere, rhizoplane, phyllosphere, phylloplane and seeds of maize (Zea mays L.) plants cultivated in different localities in Assiut Governorate (Abnob, Elbadary, Elfath, Assiut and El qosea).The isolates belonging to 15 genera, 35 species and one variety. The most dominant genus was Aspergillus whereas the most common species were A. terreus and A. flavus. A representative isolates of A. terreus were tested for riboflavin production using two different types of synthetic media. It was observed that most isolates (9 out of 12 isolates) produced riboflavin, but the highest yield on YPD medium (60 mg/l) obtained from A. terreus (isolate No. 9) which isolated from rhizoplane of maize plants.

A total of 230 fungal isolates were recovered from rhizosphere, rhizoplane, phyllosphere, phylloplane and seeds of maize (Zea mays L.) plants cultivated in different localities in Assiut Governorate (Abnob, Elbadary, Elfath, Assiut and El qosea).The isolates belonging to 15 genera, 35 species and one variety. The most dominant genus was Aspergillus whereas the most common species were A. terreus and A. flavus. A representative isolates of A. terreus were tested for riboflavin production using two different types of synthetic media. It was observed that most isolates (9 out of 12 isolates) produced riboflavin, but the highest yield on YPD medium (60 mg/l) obtained from A. terreus (isolate No. 9) which isolated from rhizoplane of maize plants.

A total of 230 fungal isolates were recovered from rhizosphere, rhizoplane, phyllosphere, phylloplane and seeds of maize (Zea mays L.) plants cultivated in different localities in Assiut Governorate (Abnob, Elbadary, Elfath, Assiut and El qosea).The isolates belonging to 15 genera, 35 species and one variety. The most dominant genus was Aspergillus whereas the most common species were A. terreus and A. flavus. A representative isolates of A. terreus were tested for riboflavin production using two different types of synthetic media. It was observed that most isolates (9 out of 12 isolates) produced riboflavin, but the highest yield on YPD medium (60 mg/l) obtained from A. terreus (isolate No. 9) which isolated from rhizoplane of maize plants.

Forty-nine species and two species varieties belonging to 22 genera isolated on glucose and 1% crude oil Czapek's agar medium from 48 soil samples contaminated with mazot and solar collected from three governorates in Upper Egypt namely, El-Minya, Assiut and Sohag. The most common genus was Aspergillus which isolated from three governorates and from both soil types, while the most common species was Aspergillus fumigatus on mazot polluted soil and Aspergillus flavus, Aspergillus fumigatus and Aspergillus terreus on solar polluted soils. Out of these fungal species, 40 isolates were tested for their ability to utilize crude oil in liquid culture at 28 ±1ºC. Only 32 isolates subjected to lipase activity test. Remarkably, on these tested isolates 35 isolate have been grown, 5 isolates have been growing without producing the enzyme and 5 isolates not grown. The highest lipase activity observed by Fusarium verticilloides giving 12.28 U/ml.